Adjustment of Operating Times by Delays using a Monte Carlo Approach

Source: R/mcs_delay.R

In general, the amount of available information about units in the field is very different. During the warranty period, there are only a few cases with complete data (mainly failed units) but lots of cases with incomplete data (usually censored units). As a result, the operating time of units with incomplete information is often inaccurate and must be adjusted by delays.

This function reduces the operating times of incomplete observations by simulated delays (in days). A unit is considered as incomplete if the later of the related dates is unknown. See 'Details' for some practical examples.

Random delay numbers are drawn from the distribution determined by complete cases (described in 'Details' of dist_delay).

# S3 method for default
mcs_delay(
  ...,
  date_1,
  date_2,
  time,
  status = NULL,
  id = paste0("ID", seq_len(length(time))),
  distribution = c("lognormal", "exponential")
)

Arguments

...

Further arguments passed to or from other methods. Currently not used.

date_1

A vector of class character or Date, in the format "yyyy-mm-dd", representing the earlier of the two dates belonging to a particular delay. Use NA for missing elements.

If more than one delay is to be considered, use a list where the first element is the earlier date of the first delay, the second element is the earlier date of the second delay, and so forth (see 'Examples').

date_2

A vector of class character or Date in the format "yyyy-mm-dd". date_2 is the counterpart of date_1 and is used the same as date_1, just with the later date(s) of the particular delay(s). Use NA for missing elements.

time

Operating times. Use NA for missing elements.

status

Optional argument. If used, it must contain binary data (0 or 1) indicating whether a unit is a right censored observation (= 0) or a failure (= 1).

If status is provided, class wt_reliability_data is assigned to the output of mcs_delay, which enables the direct application of estimate_cdf on operating times.

id

Identification of every unit.

distribution

Supposed distribution of the respective delay.

Value

A list with class wt_mcs_delay containing the following elements:

  • data : A tibble returned by mcs_delay_data where two modifications has been made:

    • If the column status exists, the tibble has additional classes wt_mcs_data and wt_reliability_data. Otherwise, the tibble only has the additional class wt_mcs_data (which is not supported by estimate_cdf).

    • The column time is renamed to x (to be in accordance with reliability_data) and contains the adjusted operating times for incomplete observations and input operating times for the complete observations.

  • sim_data : A tibble with column sim_delay that holds the simulated delay-specific numbers for incomplete cases and 0 for complete cases. If more than one delay was considered multiple columns with names sim_delay_1, sim_delay_2, ..., sim_delay_i and corresponding delay-specific random numbers are presented.

  • model_estimation : A list returned by dist_delay.

Details

In field data analysis time-dependent characteristics (e.g. time in service) are often imprecisely recorded. These inaccuracies are caused by unconsidered delays.

For a better understanding of the MCS application in the context of field data, two cases are described below.

  • Delay in registration: It is common that a supplier, which provides parts to the manufacturing industry does not know when the unit, in which its parts are installed, were put in service (due to unknown registration or sales date (date_2)). Without taking the described delay into account, the time in service of the failed units would be the difference between the repair date and the production date (date_1) and for intact units the difference between the present date and the production date. But the real operating times are (much) shorter, since the stress on the components have not started until the whole systems were put in service. Hence, units with incomplete data (missing date_2) must be reduced by the delays.

  • Delay in report:: Authorized repairers often do not immediately notify the manufacturer or OEM of repairs that were made during the warranty period, but instead pass the information about these repairs in collected forms e.g. weekly, monthly or quarterly. The resulting time difference between the reporting (date_2) of the repair in the guarantee database and the actual repair date (date_1), which is often assumed to be the failure date, is called the reporting delay. For a given date where the analysis is made there could be units which had a failure but the failure isn't reported and therefore they are treated as censored units. In order to take this into account and according to the principle of equal opportunities, the lifetime of units with missing report date (date_2[i] = NA) is reduced by simulated reporting delays.

References

Verband der Automobilindustrie e.V. (VDA); Qualitätsmanagement in der Automobilindustrie. Zuverlässigkeitssicherung bei Automobilherstellern und Lieferanten. Zuverlässigkeits-Methoden und -Hilfsmittel.; 4th Edition, 2016, ISSN:0943-9412

See also

dist_delay for the determination of a parametric delay distribution and estimate_cdf for the estimation of failure probabilities.

Examples

# Example 1 - MCS for delay in registration:
mcs_regist <- mcs_delay(
  date_1 = field_data$production_date,
  date_2 = field_data$registration_date,
  time = field_data$dis,
  status = field_data$status,
  distribution = "lognormal"
)

# Example 2 - MCS for delay in report:
mcs_report <- mcs_delay(
  date_1 = field_data$repair_date,
  date_2 = field_data$report_date,
  time = field_data$dis,
  status = field_data$status,
  distribution = "exponential"
)
#> Warning: At least one of the date differences is less than or equal to 0 and is ignored for the estimation step!

# Example 3 - Reproducibility of random numbers:
set.seed(1234)
mcs_report_reproduce <- mcs_delay(
  date_1 = field_data$repair_date,
  date_2 = field_data$report_date,
  time = field_data$dis,
  status = field_data$status,
  distribution = "exponential"
)
#> Warning: At least one of the date differences is less than or equal to 0 and is ignored for the estimation step!

# Example 4 - MCS for delays in registration and report with same distribution:
mcs_delays <- mcs_delay(
  date_1 = list(field_data$production_date, field_data$repair_date),
  date_2 = list(field_data$registration_date, field_data$report_date),
  time = field_data$dis,
  status = field_data$status,
  distribution = "lognormal"
)
#> Warning: At least one of the date differences is less than or equal to 0 and is ignored for the estimation step!

# Example 5 - MCS for delays in registration and report with different distributions:
## Assuming lognormal registration and exponential reporting delays.
mcs_delays_2 <- mcs_delay(
  date_1 = list(field_data$production_date, field_data$repair_date),
  date_2 = list(field_data$registration_date, field_data$report_date),
  time = field_data$dis,
  status = field_data$status,
  distribution = c("lognormal", "exponential")
)
#> Warning: At least one of the date differences is less than or equal to 0 and is ignored for the estimation step!